An Anticipating Calculus Approach to the Utility Maximization of an Insider

In this paper we consider a financial market with an insider that has, at time   t = 0  , some additional information of the whole developing of the market. We use the forward integral, which is an anticipating integral, and the techniques of the Malliavin calculus so that we can take advantage of the privileged information to maximize the expected logarithmic utility from terminal wealth.     

Additional utility of insiders with imperfect dynamical information

In this paper we consider a market driven by a Wiener process where there is an insider and a regular trader. The insider has privileged information which has been deformed by an independent noise vanishing as the revelation time approaches. At this time, the information of every trader is the same. We obtain the semimartingale decomposition of the original Wiener process under dynamical enlargement of the filtration, and we prove that if the rate at which the additional noise in the insiders information vanishes is slow enough then there is no arbitrage and the additional utility of the insider is finite.Received: 1 October 2003, Mathematics Subject Classification: 60G48, 90A09, 60H07, 90A60JEL Classification: D82, G11, G14     

Completion of a Lévy market by power-jump assets

Except for the geometric Brownian model and the geometric Poissonian model, the general geometric Lévy market models are incomplete models and there are many equivalent martingale measures. In this paper we suggest to enlarge the market by a series of very special assets (power-jump assets) related to the suitably compensated power-jump processes of the underlying Lévy process. By doing this we show that the market can be completed. The very particular choice of the compensators needed to make these processes tradable is delicate. The question in general is related to the moment problem.Received: June 2004, Mathematics Subject Classification (2000): 91B28, 91B26, 91B16, 91B70JEL Classification: C61The work of José Manuel Corcuera and David Nualart is partially supported by the MCyT grant no. BFM200304294. W. Schoutens is a Postdoctoral Fellow of the Fund for Scientific Research - Flanders (Belgium) (F.W.O. - Vlaanderen).